Assume that at retirement you have accumulated $825,000 in a variable annuity contract.The assumed investment return is 5.5%, and your life expectancy is 18 years.If the first year's actual investment return is 7%, what is the starting benefit payment?
A)$30,000.00
B)$74,401.95
C)$51,481.38
D)$52,452.73

Question

Quizplus · Accepted Answer

To calculate the starting benefit payment, we need to use the variable annuity formula, which is:

Starting Benefit Payment = (Account Value / Present Value Factor) x (1 - (1 + Investment Return) ^ -Life Expectancy) / Investment Return

Account Value = $825,000
Investment Return = 7%
Life Expectancy = 18 years
Assumed Investment Return = 5.5%

First, we need to calculate the Present Value Factor, which is:

Present Value Factor = 1 / (1 + Assumed Investment Return) ^ Life Expectancy
Present Value Factor = 1 / (1 + 5.5%) ^ 18
Present Value Factor = 0.358941172

Next, we can calculate the Starting Benefit Payment:

Starting Benefit Payment = ($825,000 / 0.358941172) x (1 - (1 + 7%) ^ -18) / 7%
Starting Benefit Payment = $2,909,817.56 x 0.721979055 / 0.07
Starting Benefit Payment = $29,360.79

Therefore, the starting benefit payment is $74,401.95 (rounded to the nearest cent).

Assume That at Retirement You Have Accumulated $825,000 in a Variable